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Theorem oplem1 881
Description: A specialized lemma for set theory (ordered pair theorem). (Contributed by NM, 18-Oct-1995.) (Proof shortened by Wolf Lammen, 8-Dec-2012.) (Proof shortened by Mario Carneiro, 2-Feb-2015.)
Hypotheses
Ref Expression
oplem1.1
oplem1.2
oplem1.3
oplem1.4
Assertion
Ref Expression
oplem1

Proof of Theorem oplem1
StepHypRef Expression
1 oplem1.1 . 2
2 idd 21 . . 3
3 oplem1.2 . . . . 5
4 ax-1 5 . . . . . 6
5 oplem1.4 . . . . . . 7
65biimprcd 149 . . . . . 6
74, 6jaoi 635 . . . . 5
83, 7syl 14 . . . 4
9 oplem1.3 . . . 4
108, 9syl6ibr 151 . . 3
112, 10jaod 636 . 2
121, 11mpd 13 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  preqr1g  3528  preqr1  3530
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